{"paper":{"title":"Stability of Compensated Jump Integrals under Quadratic Variation Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Kennerberg","submitted_at":"2026-05-12T08:50:24Z","abstract_excerpt":"We study the stability of compensated jump integrals under convergence of quadratic variation alone. Let \\(X\\) and \\(\\{X^n\\}_{n\\ge1}\\) be c\\`adl\\`ag processes with jump measures \\(\\mu,\\mu_n\\) and predictable compensators \\(\\nu,\\nu_n\\). Under the assumption \\[ [X^n-X]_t \\to 0 \\qquad\\text{in probability}, \\] we establish ucp convergence of compensated jump integrals of the form \\[ \\int_0^. \\int_{\\mathbb R} f_n(s,x)(\\mu_n-\\nu_n)(ds,dx) \\] under local linear growth and locally uniform convergence assumptions on the integrands.\n  The proof is based on two structural mechanisms. The first is a forbi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under the assumption [X^n - X]_t → 0 in probability, we establish ucp convergence of compensated jump integrals of the form ∫_0^. ∫_R f_n(s,x)(μ_n - ν_n)(ds,dx) under local linear growth and locally uniform convergence assumptions on the integrands.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The integrands f_n satisfy local linear growth and locally uniform convergence; the forbidden bands principle and compensator mass control hold based on quadratic variation convergence alone.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quadratic variation convergence alone implies ucp convergence of compensated jump integrals for cadlag processes under local linear growth and locally uniform integrand conditions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ce02aa37b7aeef6f0e220c485c383ed621ac9b0ea1eaa0693db079fda84e6383"},"source":{"id":"2605.11783","kind":"arxiv","version":2},"verdict":{"id":"ceba67b5-cada-4f72-8878-cbff5510d5d6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T05:20:13.124028Z","strongest_claim":"Under the assumption [X^n - X]_t → 0 in probability, we establish ucp convergence of compensated jump integrals of the form ∫_0^. ∫_R f_n(s,x)(μ_n - ν_n)(ds,dx) under local linear growth and locally uniform convergence assumptions on the integrands.","one_line_summary":"Quadratic variation convergence alone implies ucp convergence of compensated jump integrals for cadlag processes under local linear growth and locally uniform integrand conditions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The integrands f_n satisfy local linear growth and locally uniform convergence; the forbidden bands principle and compensator mass control hold based on quadratic variation convergence alone.","pith_extraction_headline":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11783/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T22:31:31.787536Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T13:25:04.295129Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-20T03:42:00.316125Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T11:37:40.294895Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"65aa5fe3a403ebc6026dc7196c757fbeecb57ffd4a0248486b03439bee979842"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"fbae2c76271cf4909201f05bde09f74113ad6a0de019d17166b816d45003d128"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}